Formalizing common sense reasoning for scalable inconsistency-robust information coordination using Direct Logic™ Reasoning and the Actor Model

Carl Hewitt (1)

1 MOHC - Met Office Hadley Centre

Because contemporary large software systems are pervasively inconsistent, it is not safe to reason about them using classical logic. The goal of Direct Logic is to be a minimal fix to classical mathematical logic that meets the requirements of large-scale Internet applications (including sense making for natural language) by addressing the following issues: inconsistency robustness, contrapositive inference bug, and direct argumentation. Direct Logic makes the following contributions over previous work: * Direct Inference (no contrapositive bug for inference) * Direct Argumentation (inference directly expressed) * Inconsistency-robust deduction without artifices such as indices (labels) on propositions or restrictions on reiteration * Intuitive inferences hold including the following: * Boolean Equivalences * Reasoning by splitting for disjunctive cases * Soundness * Inconsistency-robust Proof by Contradiction Since the global state model of computation (first formalized by Turing) is inadequate to the needs of modern large-scale Internet applications the Actor Model was developed to meet this need. Using, the Actor Model, this paper proves that Logic Programming is not computationally universal in that there are computations that cannot be implemented using logical inference. Consequently the Logic Programming paradigm is strictly less general than the Procedural Embedding of Knowledge paradigm.

Mots clés: Direct Logic; Inconsistency Robustness; Mathematical Logic

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Mathématiques générales [math.GM]; Logique [math.LO]

Carl Hewitt. Formalizing common sense reasoning for scalable inconsistency-robust information coordination using Direct Logic™ Reasoning and the Actor Model. Inconsistency Robustness, 2015, 978-1-84890-159-9. ⟨hal-01148501v1⟩